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Scale functions and tree ends

Part of: Locally compact groups and their algebras

Published online by Cambridge University Press:  09 April 2009

A. Kepert  and
G. Willis
A. Kepert
Affiliation:
School of Science and Technology University of NewcastleOurimbah NSW 2258Australia e-mail: andrew@maths.newcastle.edu.au
G. Willis
Affiliation:
School of Mathematical and Physical Sciences University of NewcastleCallaghan NSW 2308Australia e-mail: george@maths.newcastle.edu.au
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Abstract

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A class of totally disconnected groups consisting of partial direct products on an index set is examined. For such a group, the scale function is found, and for automorphisms arising from permutations of the index set, the tidy subgroups are characterised. When applied to the case where the index set is a finitely-generated free group and the permutation is translation by an element x of the group, the scale depends on the cyclically reduced form of x and the tidy subgroup on the element which conjugates x to its cyclically reduced form.

MSC classification

Secondary: 22D05: General properties and structure of locally compact groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 2 , April 2001 , pp. 273 - 292
Copyright
Copyright © Australian Mathematical Society 2001

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